python二維正態分佈

# -*- coding:utf-8 -*-
import numpy as np from scipy import stats import math import matplotlib as mpl import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm def calc_statistics(x): n = x.shape[0] #樣本個數
 m = 0#指望
    m2 = 0#平方的指望
    m3 = 0#三次方的指望
    m4 = 0#四次方的指望
    for t in x: #向量的加法
        m += t m2 += t*t m3 += t**3 m4 += t**4 m /= n m2 /= n m3 /= n m4 /= n #標準差 = E((X - E(X))^2) = E(X^2) - E(X)^2
    sigma = np.sqrt(m2-m*m) #求偏度 = E((X-E(X))^3) = (m3 - 3*m*m2 + 2*m**3) / sigma**3
    skew = (m3 - 3*m*sigma**2 - m**3) / sigma**3
    #求峯度
    kurtosis = m4 / sigma**4 - 3
    print('手動計算均值、標準差、偏度、峯度：', m, sigma, skew, kurtosis) #使用系統函數驗證
    mu = np.mean(x,axis=0) sigma = np.std(x,axis=0) skew = stats.skew(x) kurtosis = stats.kurtosis(x) return mu,sigma,skew,kurtosis if __name__ == '__main__': # d = np.random.randn(100000)
    # print(d)
    # mu, sigma, skew, kurtosis = calc_statistics(d)
    # print('函數計算均值、標準差、偏度、峯度：', mu, sigma, skew, kurtosis)
    # # 一維直方圖
    # mpl.rcParams[u'font.sans-serif'] = 'SimHei'
    # mpl.rcParams[u'axes.unicode_minus'] = False
    # #畫出統計直方圖
    # #bins直方圖的條數
    # #density=True 畫出趨勢圖
    # #y1:x1每一箇中每一個值出現的次數的度量
    # #x1:d的值的範圍
    # y1, x1, dummy = plt.hist(d, bins=50,density=True, color='g', alpha=0.75)
    # t = np.arange(x1.min(), x1.max(), 0.05)
    # #繪製標準正態分佈的曲線
    # y = np.exp(-t ** 2 / 2) / math.sqrt(2 * math.pi)
    # plt.plot(t, y, 'r-', lw=2)
    # plt.title(u'高斯分佈，樣本個數：%d' % d.shape[0])
    # plt.grid(True)
    # plt.show()

    #二維
    print("二維正態分佈") d = np.random.randn(100000, 2) mu, sigma, skew, kurtosis = calc_statistics(d) print('函數計算均值、標準差、偏度、峯度：', mu, sigma, skew, kurtosis) # 二維圖像
    N = 50
    #density：edges中每一個值出現的次數的度量
    density, edges = np.histogramdd(d, bins=[N, N]) print('樣本總數：', np.sum(density)) density /= density.max() x = y = np.arange(N) t = np.meshgrid(x, y) fig = plt.figure(facecolor='gray') ax = fig.add_subplot(111, projection='3d') #x,y,z
    ax.scatter(t[0], t[1], density, c='r', s=15 * density, marker='o', depthshade=True) # ax.plot_surface(t[0], t[1], density, cmap=cm.Accent, rstride=2, cstride=2, alpha=0.9, lw=0.75)
    # ax.set_xlabel(u'X')
    # ax.set_ylabel(u'Y')
    # ax.set_zlabel(u'Z')
    # plt.title(u'二元高斯分佈，樣本個數：%d' % d.shape[0], fontsize=20)
    # plt.tight_layout(0.1)
    plt.show()

# -*- coding:utf-8 -*-
import numpy as np from scipy import stats import math import matplotlib as mpl import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm def calc_statistics(x): n = x.shape[0] #樣本個數
 m = 0#指望
    m2 = 0#平方的指望
    m3 = 0#三次方的指望
    m4 = 0#四次方的指望
    for t in x: #向量的加法
        m += t m2 += t*t m3 += t**3 m4 += t**4 m /= n m2 /= n m3 /= n m4 /= n #標準差 = E((X - E(X))^2) = E(X^2) - E(X)^2
    sigma = np.sqrt(m2-m*m) #求偏度 = E((X-E(X))^3) = (m3 - 3*m*m2 + 2*m**3) / sigma**3
    skew = (m3 - 3*m*sigma**2 - m**3) / sigma**3
    #求峯度
    kurtosis = m4 / sigma**4 - 3
    print('手動計算均值、標準差、偏度、峯度：', m, sigma, skew, kurtosis) #使用系統函數驗證
    mu = np.mean(x,axis=0) sigma = np.std(x,axis=0) skew = stats.skew(x) kurtosis = stats.kurtosis(x) return mu,sigma,skew,kurtosis if __name__ == '__main__': # d = np.random.randn(100000)
    # print(d)
    # mu, sigma, skew, kurtosis = calc_statistics(d)
    # print('函數計算均值、標準差、偏度、峯度：', mu, sigma, skew, kurtosis)
    # # 一維直方圖
    # mpl.rcParams[u'font.sans-serif'] = 'SimHei'
    # mpl.rcParams[u'axes.unicode_minus'] = False
    # #畫出統計直方圖
    # #bins直方圖的條數
    # #density=True 畫出趨勢圖
    # #y1:x1每一箇中每一個值出現的次數的度量
    # #x1:d的值的範圍
    # y1, x1, dummy = plt.hist(d, bins=50,density=True, color='g', alpha=0.75)
    # t = np.arange(x1.min(), x1.max(), 0.05)
    # #繪製標準正態分佈的曲線
    # y = np.exp(-t ** 2 / 2) / math.sqrt(2 * math.pi)
    # plt.plot(t, y, 'r-', lw=2)
    # plt.title(u'高斯分佈，樣本個數：%d' % d.shape[0])
    # plt.grid(True)
    # plt.show()

    #二維
    print("二維正態分佈") d = np.random.randn(100000, 2) mu, sigma, skew, kurtosis = calc_statistics(d) print('函數計算均值、標準差、偏度、峯度：', mu, sigma, skew, kurtosis) # 二維圖像
    N = 50
    #density：edges中每一個值出現的次數的度量
    density, edges = np.histogramdd(d, bins=[N, N]) print('樣本總數：', np.sum(density)) density /= density.max() x = y = np.arange(N) t = np.meshgrid(x, y) fig = plt.figure(facecolor='gray') ax = fig.add_subplot(111, projection='3d') #x,y,z
    ax.scatter(t[0], t[1], density, c='r', s=15 * density, marker='o', depthshade=True) # ax.plot_surface(t[0], t[1], density, cmap=cm.Accent, rstride=2, cstride=2, alpha=0.9, lw=0.75)
    # ax.set_xlabel(u'X')
    # ax.set_ylabel(u'Y')
    # ax.set_zlabel(u'Z')
    # plt.title(u'二元高斯分佈，樣本個數：%d' % d.shape[0], fontsize=20)
    # plt.tight_layout(0.1)
    plt.show()